Abstract
Amorphous materials distinguish themselves from crystalline materials by lacking long-range order while retaining structural order at the local scale (2–5 Å). However, the complexity in topological and chemical order prevents current characterization tools from fully unveiling the structure in disordered materials. Consequently, the nature of medium-range order in amorphous materials has remained elusive. The Zachariasen and crystal competing models have been proposed to describe disordered phases and have both been verified through synthesis and characterization. The main difference between them is thought to be whether the amorphous phase shows medium-range order. Here we demonstrate a form of organized inorganic matter that is amorphous in two dimensions, while exhibiting long-range order and a high degree of crystallinity in the third. The structure consists of periodically stacked 2-dimensional amorphous Nb-W-O monolayers without long-range in-plane order. The unique periodic and therefore crystalline stacking along one principal axis enables direct imaging and revealed that the amorphous Nb-W-O monolayers formed in agreement with the Zachariasen model for 2 dimensions. Our findings show that the gap between crystalline and amorphous materials does not only depend on medium-range order but can also apply to principal dimensions within the same solid.
Data availability
The authors declare that the data and images supporting the findings of this study are available at Zenodo repository: https://doi.org/10.5281/zenodo.17588010.
References
Elliott, S. R. Medium-range structural order in covalent amorphous solids. Nature 354, 445–452 (1991).
Price, D. L. Intermediate-range order in glasses. Curr. Opin. Solid State Mat. Sci. 1, 572–577 (1996).
Salmon, P. S. et al. Topological versus chemical ordering in network glasses at intermediate and extended length scales. Nature 435, 75–78 (2005).
Mavracic, J. et al. Similarity between amorphous and crystalline phases: the case of TiO2. J. Phys. Chem. Lett. 9, 2985–2990 (2018).
Toh, C.-T. et al. Synthesis and properties of free-standing monolayer amorphous carbon. Nature 577, 199–203 (2020).
Gibson, J. M. et al. Substantial crystalline topology in amorphous silicon. Phys. Rev. Lett. 105, 125504 (2010).
Joo, W. J. et al. Realization of continuous Zachariasen carbon monolayer. Sci. Adv. 3, e1601821 (2017).
Huang, P. Y. et al. Direct imaging of a two-dimensional silica glass on graphene. Nano Lett. 12, 1081–1086 (2012).
Huang, P. Y. et al. Imaging atomic rearrangements in two-dimensional silica glass: watching silica’s dance. Science 342, 224–227 (2013).
Tian, H. F. Disorder-tuned conductivity in amorphous monolayer carbon. Nature 615, 56–61 (2023).
Wang, J. et al. Chemical medium-range order in a medium-entropy alloy. Nat. Comm. 13, 1021 (2022).
Sheng, H. W. et al. Atomic packing and short-to-medium-range order in metallic glasses. Nature 439, 419–425 (2006).
Lan, S. et al. A medium-range structure motif linking amorphous and crystalline states. Nat. Mater. 20, 1347–1352 (2021).
Hirata, A. et al. Direct observation of local atomic order in a metallic glass. Nat. Mater. 10, 28–33 (2011).
Hou, J. W. et al. Liquid-phase sintering of lead halide perovskites and metal-organic framework glasses. Science 374, 621–625 (2021).
Zachariasen, W. H. The atomic arrangement in glass. J. Am. Chem. Soc. 54, 3841–3851 (1932).
Tu, Y. H. et al. Properties of a continuous-random-network model for amorphous systems. Phys. Rev. Lett. 81, 4899 (1998).
Yang, Y. et al. Determining the three-dimensional atomic structure of an amorphous solid. Nature 592, 60–64 (2021).
Yuan, Y. K. et al. Three-dimensional atomic packing in amorphous solids with liquid-like structure. Nat. Mater. 21, 95–102 (2022).
Treacy, M. M. J. & Borisenko, K. B. The local structure of amorphous silicon. Science 335, 950–953 (2012).
MozeticÏ, M. et al. A method for the rapid synthesis of large quantities of metal oxide nanowires at low temperatures. Adv. Mater. 17, 2138 (2005).
Jana, S. & Rioux, R. M. Seeded growth induced amorphous to crystalline transformation of niobium oxide nanostructures. Nanoscale 4, 1782 (2012).
Betzler, S. B. Atomic resolution observation of the oxidation of niobium oxide nanowires: implications for renewable energy applications. ACS Appl. Nano Mater. 3, 9285 (2020).
Krumeich, F. The complex crystal chemistry of niobium tungsten oxides. Chem. Mater. 34, 911–934 (2022).
Iijima, S. & Allpress, J. G. Structural studies by high-resolution electron microscopy: tetragonal tungsten bronze-type structures in the system Nb2O5-WO3. Acta Crystallogr. A 30, 22–29 (1974).
Iijima, S. & Allpress, J. G. Structural studies by high-resolution electron microscopy: coherent intergrowth of the ReO3 and tetragonal tungsten bronze structure types in the system Nb2O5-WO3. Acta Crystallogr. A 30, 29–36 (1974).
Krumeich, F. On the arrangement of pentagonal columns in tetragonal tungsten bronze-type Nb18W16O93. Crystals 11, 1514 (2021).
Krumeich, F. Oxidation products of Nb7W10O47: a transmission electron microscopy study. J. Solid State Chem. 119, 420–427 (1995).
de Ridder, R. et al. Application of the cluster model to the study of ordering of atom strings in ternary W-Nb oxides. Phys. Status Solidi 41, 555–560 (1977).
Iijima, S. & Cowley, J. M. Studies of ordering using high resolution electron microscopy. J. Phys. Colloq. 38, C7–135 (1977).
Horiuchi, S., Muramatsu, K. & Matsui, Y. Circular diffuse scattering from a niobium tungsten bronze, 3Nb2O5.8WO3, studied by 1 MV high-resolution electron microscopy. J. Appl. Crystallogr. 13, 141–147 (1980).
de Ridder, R. et al. A cluster model for the transition state and its study by means of electron diffraction I. theoretical model. Phys. Status Solidi 38, 663–674 (1976).
Krumeich, F. Order and Disorder in niobium tungsten oxides of the tetragonal tungsten bronze type. Acta Crystallogr. B 54, 240–249 (1998).
Krumeich, F., Bartsch, C. & Gruehn, R. Oxidation products of Nb4W13O47: a transmission electron microscopy study. J. Solid State Chem. 120, 268–274 (1995).
Krumeich, F. TEM Evidence of a new tetragonal tungsten bronze superstructure. Z. Kristallogr. 212, 708–711 (1997).
Krumeich, F. & Nesper, R. Oxidation products of the niobium tungsten oxide Nb4W13O47: a high-resolution scanning transmission electron microscopy study. J. Solid State Chem. 179, 1857–1863 (2006).
Sundberg, M. & Lundberg, M. K5Nb9W2O31: A new tetragonal tungsten bronze related structure deduced from HREM images. Chem. Scr. 14, 161–168 (1988).
Iijama, S. Structural studies by high-resolution electron microscopy: intergrowth of ReO3 and tetragonal tungsten bronze type structures in the system Nb2O5-WO3. Acta Crystallogr. A 34, 922–931 (1978).
Krumeich, F. Intergrowth of niobium tungsten oxides of the tetragonal tungsten bronze type. Z. Naturforsch. B 75, 913–919 (2020).
England, P. J. & Tilley, R. J. D. An electron microscopy study of some tetragonal tungsten bronze related phases in the Nb2O5-WO3, Ta2O5-WO3 and Nb2O5-Ta2O5-WO3 systems. Chem. Scr. 23, 15–22 (1984).
Sayagués, M. J., Krumeich, F. & Hutchison, J. L. Solid-gas reactions of complex oxides inside an environmental high resolution transmission electron microscope. Micron 32, 457–471 (2001).
Xia, R. et al. Enhanced lithiation dynamics in nanostructured Nb18W16O93 anodes. J. Power Sources 482, 228898 (2021).
Wang, S. T. et al. Pre-zeolite framework super-MIEC anodes for high-rate lithium-ion batteries. Energy Environ. Sci. 16, 241–251 (2023).
Bakradze, G., Kalinko, A. & Kuzmin, A. Evidence of nickel ions dimerization in NiWO4 and NiWO4-ZnWO4 solid solutions probed by EXAFS spectroscopy and reverse Monte Carlo simulations. Acta Mater. 217, 117171 (2021).
Stephenson, N. C. & Craig, D. C. The crystal structure of Nb8W9O47. Acta Crystallogr. B 25, 2071–2083 (1969).
Stephenson, N. C. A structural investigation of some stable phases in the region Nb2O5.WO3–WO3. Acta Crystallogr. B 24, 637–653 (1968).
Hussain, A., Woerle, M. & Krumeich, F. Superstructure and twinning in the tetragonal tungsten bronze-type phase Nb7W10O47. J. Solid State Chem. 149, 428–433 (2000).
Kuczyński, W., Żywucki, B. & Małecki, J. Determination of orientational order parameter in various liquid-crystalline phases. Mol. Cryst. Liq. Cryst. 381, 1–19 (2002).
Förster, S. et al. Quasicrystals and their approximants in 2D ternary oxides. Phys. Status Solidi (B) 257, 1900624 (2020).
Ruano-Merchan, C. et al. Stoichiometry-driven formation of two-dimensional ternary oxides: from quasicrystal approximants to honeycomb lattice structures. J. Phys. Chem. C. 128, 8839 (2024).
Iijima, S. et al. Atomic resolution imaging of cation ordering in niobium–tungsten complex oxides. Comm. Mater. 2, 24 (2021).
Iijima, S., Ohnishi, I. & Liu, Z. Atomic‑resolution STEM‑EDS studies of cation ordering in Ti‑Nb oxide crystals. Sci. Rep. 11, 18022 (2021).
Hong, Y. et al. A broad-spectrum gas sensor based on correlated two-dimensional electron gas. Nat. Commun. 14, 8496 (2023).
Chahine, G. A. et al. Imaging of strain and lattice orientation by quick scanning X-ray microscopy combined with three-dimensional reciprocal space mapping. J. Appl. Crystallogr. 47, 762–769 (2014).
Acknowledgements
R.X. and J.Z. acknowledge the financial support of the China Scholarships Council (CSC) program (No. 201807720013 and No. 201906150132), respectively. K.Z. acknowledges support by the National Natural Science Foundation of China (21905169) and Guangdong Basic and Applied Basic Research Foundation (2024A1515140075). C.S acknowledges for the STEM work performed at the Nanostructure Research Center (NRC) support by the Fundamental Research Funds for the Central Universities (WUT: 2019III012GX), the State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, and the State Key Laboratory of Silicate Materials for Architectures (Wuhan University of Technology). J.L., T.L. and S.L. acknowledge the use of resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility, operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02- 06CH11357. J.Z. and M.H. acknowledge financial support from the Dutch research council (NWO) under the VICI program 19909.
Author information
Authors and Affiliations
Contributions
R.X., K.Z., J.E., and M.H. conceived the project. R.X., K.Z., J.E., and M.H. co-wrote the manuscript. R.X. and J.Z. prepared the samples. R.X. performed RHEED analysis and applied the structural analysis. J.L., Q.L., S.L., T.L., and Y.R. carried out PDF, XANES, and EXAFS experiments and J.L. and K.Z. analyzed the data. Y.B. performed RSM experiments and Y.B. and R.X. analyzed the data. H.P., R.Y., and C.S. performed STEM and EDX analysis, H.P., R.Y., R.X., and K.Z. analyzed the data. R.X., K.Z., L.Z., J.Z., J.E., and M.H. revised the manuscript. All authors discussed the results and commented on the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Communications thanks Rene Guinebretiere, Fan Zhu, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Xia, R., Li, J., Birkhölzer, Y.A. et al. Orientation-dependent mutual crystalline and amorphous order in a single phase solid. Nat Commun (2026). https://doi.org/10.1038/s41467-026-69359-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41467-026-69359-3
